2021/03/20 by Takagi, Hiromichi
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.11086
We construct a 14-dimensional affine variety Σ14_\mathbbA with a \rmGL3- and a (ℂ^*)6-actions. We denote by Σ13_\mathbbA the affine variety obtained from Σ14_\mathbbA by setting one specified variable to 1 (we refer the precise definition to Definition 1.1 of the paper). We show that several weighted projectivizations of Σ13_\mathbbA and Σ14_\mathbbA produce, as weighted complete intersections, examples of prime ℚ-Fano threefolds of codimension four belonging to 24 classes of the graded ring database. Except No.360 in the database, these prime ℚ-Fano threefolds have a Type I Tom projection. Moreover, they are not weighted complete intersections of the cluster variety of type C2 introduced by Coughlan and Ducat. We also show that a partial projectivization of Σ14_\mathbbA has a ℙ2× ℙ2-fibration over the affine space \mathbbA9.